Subgroups — C₁₃×C₃⋊Dic₅₇ #22580231

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₅₇	—	3	4	no	maximal
3	C₃²×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₁₉	D₃	1	4	yes	—
5	C₁₃×Dic₁₉	—	9	1	no	Hall
6	C₃×C₁₃×C₁₉	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₁₉	C₃⋊D₃	1	1	yes	characteristic
9	C₁₃×C₃⋊Dic₃	—	19	1	no	maximal, Hall
10	C₂×C₃²×C₁₉	C₂×C₁₃	1	1	yes	characteristic
11	C₁₃×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃²×C₁₃	D₁₉	1	1	yes	characteristic
13	Dic₅₇	—	3	4	no	—
14	C₃²×C₁₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
15	Dic₃×C₁₃	—	57	4	no	—
16	C₃²×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	D₃×C₁₃	1	4	yes	—
18	C₂×C₃×C₁₃	D₅₇	1	4	yes	—
19	Dic₁₉	—	9	1	no	Hall
20	C₃×C₁₉	Dic₃×C₁₃	1	4	yes	complemented
21	C₄×C₁₃	—	171	1	no	Hall
22	C₃×C₁₃	Dic₅₇	1	4	yes	complemented
23	C₂×C₁₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic
24	C₃⋊Dic₃	—	19	1	no	Hall
25	C₂×C₁₃	C₃⋊D₅₇	1	1	yes	characteristic
26	C₁₉	C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	C₁₃×D₁₉	1	1	yes	characteristic
28	C₁₃	C₃⋊Dic₅₇	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	57	4	no	—
30	C₃²	C₁₃×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₁₃×D₅₇	1	4	yes	—
32	C₄	—	171	1	no	Sylow
33	C₃	C₁₃×Dic₅₇	1	4	yes	complemented
34	C₂	C₁₃×C₃⋊D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₅₇
commutator, hypocenter	C₃²×C₁₉	C₄×C₁₃
Frattini	C₂	C₁₃×C₃⋊D₅₇
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₂×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃²×C₁₃×C₁₉	C₄	semidirect
6. C₃×C₁₃×C₁₉	Dic₃	semidirect
7. C₃⋊Dic₅₇	C₁₃	direct (N × H)
11. C₁₃×C₁₉	C₃⋊Dic₃	semidirect
14. C₃²×C₁₉	C₄×C₁₃	semidirect
16. C₃²×C₁₃	Dic₁₉	semidirect
20. C₃×C₁₉	Dic₃×C₁₃	semidirect
22. C₃×C₁₃	Dic₅₇	semidirect
26. C₁₉	C₁₃×C₃⋊Dic₃	semidirect
28. C₁₃	C₃⋊Dic₅₇	direct (N × H)
30. C₃²	C₁₃×Dic₁₉	semidirect
33. C₃	C₁₃×Dic₅₇	semidirect

Subgroups — C13×C3⋊Dic57 #22580231

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₃⋊Dic₅₇ #22580231